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Happiness; It is all relative?

- A study of well-being and the effect of relative and absolute

income.

Jacob Svensson

Student

Spring 2016

Master Thesis, 30 ECTS

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2 Abstract:

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Table of Contents

1. Introduction ... 4 1.1 Purpose ... 5 1.2 Contributions ... 6 1.3 Disposition ... 7 2. Background ... 7 3. Theoretical Framework ... 13 4. Method ... 17 5. Data ... 21 5.1 Variables ... 25

5.2 Descriptive Statistics & Empirical Model ... 28

6. Result ... 30

7. Discussion ... 37

8. Conclusion ... 41

9. Limitations of current study & Future research ... 42

References ... 43

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1. Introduction

Already back in the middle of the nineteenth century John Stuart Mill argued that “Men do not desire to be rich, but richer than other men”, Mill (1869). How are consumption and income related to subjective well-being? This question has become widespread not only within psychological literature but also in economical. In particular, economists tend to lean more towards the suggestion that consumers more likely evaluate the options available on the basis of relative values and not on absolute values of wealth or/and income, suggesting that utility depends on relative comparison. The definition of subjective well-being (SWB) is defined by economists such as Diener at el. (2003) as ‘the emotional and cognitive evaluation of people’s life’ which includes happiness, fulfillment and life satisfaction. Well-being, on the other hand, often refers to objective measures like income and life-expectancy.

Utility theory is built upon the assumption that more is better implying that an individual would prefer, or desire, an increase in income. This would lead individuals with high income to reach higher indifference curves. Economists often take it as self-evident that individuals’ satisfaction depends on what they have in absolute terms. There has been a lot of research about the relation between income and subjective well-being.

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One interesting part of this is the relationship between subjective well-being, absolute income and relative income where one could think of it as follows; assuming that only absolute income matters, the well-being of everyone would rise when everyone becomes richer. On the other hand if the opposite applies, such that only relative income matters, the opposite effect would occur that is that well-being would not rise when everyone gets richer since no one becomes richer relative to others or an average. From this it follows that it would be interesting to take the research further and examine the magnitude of the effects that relative and absolute income exert on SWB, especially, due to certain demographic characteristics. The relationship between subjective well-being, absolute income and relative income is what this paper is set out to examine further.

1.1 Purpose

The purpose of this thesis is to empirical test the importance of relative income for subjective well-being, on a micro level, in Sweden. More specifically this thesis aims at examine how the relationship between absolute income, relative income and subjective well-being varies among agents depending on: I) Age II) Population-density III) Highest level of education IV) Different levels of income V) Country of birth VI) Unemployment and VII) Partnership. This will be done by estimating ordered probit models of individual self-reported happiness and life satisfaction, known as Subjective Well-Being (SWB). The empirical analysis is based on the European Social Survey (ESS) containing cross national data over Europe.

The purpose of this thesis is to empirical test the importance of relative income for subjective well-being, on a micro level, in Sweden. More specifically this thesis aims at examine how relative and absolute income effect SWB among different agents depending on: I) Age II) Population-density III) Highest level of education IV) Different levels of income V) Country of birth VI) Unemployment and VII) Partnership. This will be done by estimating ordered probit models of individual self-reported happiness and life satisfaction, known as Subjective Well-Being (SWB). The empirical analysis is based on the European Social Survey (ESS) containing cross national data over Europe.

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I) Age II) Population-density III) Highest level of education IV) Different levels of income V) Country of birth VI) Unemployment and VII) Partnership. This will be done by estimating ordered probit models of individual self-reported happiness and life satisfaction, known as Subjective Well-Being (SWB). The empirical analysis is based on the European Social Survey (ESS) containing cross national data over Europe.

1.2 Contribution

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1.3 Disposition

In section 2 relevant background about subjective well-being and income are presented. Section 3 concerns theory which is followed by a method section as section 4. Data and variables are presented and discussed along with descriptive statistics in section 5. Results are presented in section 6 which are further discussed in section 7. The thesis finally concludes in section 8 which is lastly followed by limitations and future research in section 9.

2. Background

Early research highlighting this field include research such as Veblen (1899) and Duesenberry (1949). Richard Easterlin and his work, especially Easterlin (1974), on income and subjective being could perhaps be seen as the one of the first to study income and subjective well-being in a more systematic way. The famous Easterlin-Paradox has of course been revisited again several times since the nineteen-seventies when it was first induced. Easterlin (1995) revisits the paradox making the additional argument that ‘the material norms on which judgments of well-being are based increase in the same proportion as the actual income of the society’ implying that income and well-being and their relationship derives from relative income concerns or one’s relative position in society.Easterlin (2011) argues again that the paradox also holds for developing countries but also for developing countries transitioning from socialism to capitalism.

This is backed up by Fjiters at al. (2008) who make the statement that relative income concerns would be consistent with the paradox. In other words the argument implies that income might be compared to others, a social comparison, or to oneself in the past. The authors argue that those with higher income would, at some point in time, experience higher consumption and status as well making them be relatively happier.

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extending over a number of decades. Stevenson & Wolfers (2008) obtain a positive relationship between average levels of subjective well-being and GDP per capita across countries and that economic growth was linked with increasing happiness. This indicates a clear role for absolute income and a limited role for relative income when it comes to comparisons in determining well-being. 1

Hence literature on the Easterlin paradox includes studies such as Veenhoven (1991), Fjiters at al. (2008) and Stevenson & Wolfers (2008) which could be seen as the two sides of a coin, one relative and one absolute. This gives an indication of that both absolute and relative income affect subjective well-being.

Oswald and Clark (1995) provide a test on whether happiness depends upon a comparison level of income. By using data of self-reported levels of satisfaction for 5,500 British workers containing answers on the question: "All things considered, how satisfied or dissatisfied are you with your present job overall using the same 1-7 scale?". The data of individuals’ reported satisfaction levels is treated as measure of utility. Moreover Oswald and Clark (1995) argues that the reason to study subjective assessments of satisfaction is that it is expected to be correlated with observable actions and events. This is backed up by previous literature such as Clegg et al. (1978) and Palmore (1969) which found strong correlations between job satisfaction and; I) poor mental health II) Length of life. Oswald and Clark (1995) define the utility of an individual from working as a function of income, hours of work, individual parameters and other job parameters, where utility is measured as the level of job-satisfaction reported from the individual. Another utility model was also defined, by Oswald and Clark (1995), with the alteration of introducing a comparison or reference income level which the individual compares himself or herself to, cetris paribus. The idea was to capture effects such as relative deprivation, envy, jealousy or inequity. The first utility model is considered to be of economic standard model whereas the latter is of a more psychological design.

Moreover Oswald and Clark (1995) calculated the correspondents’ reference income by estimating an equation for earnings over the cross-section of employees, using ordered probit techniques. This was used to predict an earnings level for each person corresponding to the income for an ‘average’ employee, given typical characteristics such as education level and age.

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Furthermore relative income was finally expressed as the ratio between the absolute income and the reference income. Oswald and Clark (1995) found two things of interest; the satisfaction levels reported was found to be negatively related to their reference income. Secondly, and maybe more interesting, satisfaction was found to decline in the level of education when holding income constant. One possible explanation of the latter finding, that perhaps should be viewed with caution, is that education could induce higher aspirations.2

Another interesting study on subjective well-being is Mcbride (2001) who finds evidence, on a micro-level, that relative income does matter in individuals’ assessments of subjective well-being. Mcbride (2001) starts by highlighting the difference between the two similar but not alike concepts well-being and subjective well-being (SWB). Well-being is often referred to by economists and refers to objective measures like income and life-expectancy. Subjective well- being refers to the individual’s all parts of his/hers life where the individual is to express his/hers level of SWB. Mcbride (2001) uses data from the general social survey (GSS) and more specifically from the 1994 survey with over 2000 observations. This is narrowed down to 324 observations after one of the following criteria was meet: ‘income over $75,000, no levels of education recorded, no health status recorded, no marital status recorded, no happiness measure recorded, and no response to the question about parents’ standard of living. All observations for a respondent under 25 years of age was also dropped due to that the ‘external cohort norm, stated above, begins at age 25’.

Furthermore Mcbride (2001) identifies a potential problem with income measures since no exact figures of income was recorded. Instead individuals’ income was recorded by in which income range they fell. This was solved by creating a variable equal to the middle income of the respondent’s income range. Furthermore the reference income of individual i was defined as ‘the average income of everyone from 5 years younger than individual i to 5 years older’. This idea is based on that individual i, interacts and associates with people of similar age, in the same country, making the individual compare the own income to theirs. The self-reported measure of happiness was obtained by the question: “Taken all together, how would you say things are these days? Would you say that you are very happy, pretty happy, or not too happy?”. Due to the ordinal nature of the happiness measure an ordered probit procedure was used. Characteristics like health, sex, race, and family status were also included in the model to

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capture differences in preferences among individuals. Mcbride (2001) finds evidence indicating that an increase in relative-income norms, namely a subjective assessment of how the respondent’s current standard of living compares to past standard, affect subjective well-being negatively whilst increases in absolute income affect SWB positively. As the respondent’s income increases the strength of these effects may change implying that at higher income levels, the relative income effects appear stronger, making absolute income become more important at lower income levels as the effect of relative income is then smaller.

The relative concept is not limited to income, relative concepts can be found elsewhere as well. Alpizar at el. (2005) find, using survey-experimental methods analyzed with ordered probit techniques, that the SWB of a majority of individuals’ are affected by both relative income and relative consumption of particular goods. Data consisted of interviews with 325 student from the university of Costa Rica and consisted of three parts. One part contained questions regarding the socioeconomic status of the respondent. The other two parts were designed to examine the respondent’s relationship to relative income and relative consumption. To be more specific the relative consumption segment was constructed in the way that respondents were asked to place their, imaginary, grandchildren in a future society. The society was described by the average consumption and the grandchild’s consumption of particular good, cetris paribus. Alpizar at el. (2005) found that visible goods such as houses and cars were more positional than non-visible goods such as vacation and insurance. Additional results suggest that consumers are also positional in terms of income and that women care relatively more about status than men do. Alpizar et al. (2005) also found the concern for status to be decreasing in the parents income and discussed the possibility that status is relatively more important for individuals’ experiencing low status, i.e. decreasing returns to status. We can see that status is found to be a part of determining individual well-being. Hence, the concern for status could be a possible explanation of why people tend to compare consumption and income, at least in part.

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bracket (+/- 5 years) as the respondent concerned, same gender, similar education and living in the same country to measure reference income. Caporale et al. (2007) use ‘life satisfaction’ as the measure of well-being and thus as their dependent variable but were also running regressions using ‘happiness’ as the dependent variable. They argue that self-reported happiness and life satisfaction might capturing different things about an individual’s subjective well-being. Life satisfaction would be referring to what one would call a cognitive state (or cognitive states) of consciousness, whereas happiness would be referring to emotional concerns and profound matters of life. The original idea was brought out by Michalos (1991) who argue that it would be heuristically useful to measure and analyze ‘happiness’ and ‘life satisfaction’ separately, which also is backed up by latter research such as Gundelach (2004). Caporale et al. (2007) furthermore assume that the unobserved level of utility is related to the observed personal characteristics and income. Ordered probit models were estimated due to the ordinal nature of their dependent variable, taking values from 1 to 10.

Furthermore Caporale et al (2007) found that income of a reference group would have a negative effect on the self-reported SWB, which also was the case after controlling for absolute income and other demographic characteristics, such as education, age, unemployment. More findings suggested that women are more likely to report higher level of life satisfaction than men and that life satisfaction exhibits a U-shaped relationship with age. The latter finding could be explained by shifting life-cycle aspects of individuals’ social, family and economic circumstances which is discussed in other literature as well, such as Alesina et al. (2004). A change in family circumstances, for example, such as having children or divorce might change an individuals’ preferences.

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to be more ‘pronounced’ for the latter category. Furthermore individuals were split into two groups based on the level of education. By running separate regressions individuals’ with higher education were found to derive higher levels of life satisfaction from an increase in absolute income.

The effect of reference income between different countries and regions might differ, as suggested by Caporale et al (2007). Other research such as Ferrer-i-Carbonell (2005) examines various hypotheses about subjective well-being and income. More specifically Ferrer-i-Carbonell (2005) examines: the importance of absolute income, the importance of reference income, the effect exerted form the distance between absolute income and reference income and finally how the comparison effect of income differs between rich and poor individuals. The study is based on the German Socio-Economic Panel were the sample includes almost 16 000 respondents, West and (former) East Germans are also distinguished between in the study. Reported life satisfaction is used as a measure of subjective well-being where an ordered probit is used for estimation. The question on life satisfaction is stated as follows: “How happy are you at present with your life as a whole?” Ferrer-i-Carbonell (2005) defines the reference group based on those with similar education, inside the same age bracket (younger than 25, 25–34, 35–44, 45–65, and 66 or older), and living in the same region. Absolute income is operationalized as family income or the household’s income stated as a net value after tax deduction.

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More research concerning comparison perspectives were done by Greeta et al. (2005) and Luttmer (2004). Conducted on a South African data set Greeta et al. (2005) found, in part, evidence of that relative income would affect subjective well-being differently depending on the distance to comparative others. Greeta et al. (2005) argue that income of a reference group close to the respondent would exert a positive effect on subjective well-being. Comparative income of a reference group far away, i.e. located in a distance, on the other hand would exert a negative effect on subjective well-being. Luttmer (2004) investigated whether one did feel worst of when being around others that earn more than oneself using panel data on an individual-level. Luttmer (2004) found that lower levels of self-reported happiness were associated with higher earnings of one’s neighbors. Luttmer (2004) argues that this effect most likely is caused by interpersonal preferences implying that self-reported happiness would be dependent on the relative consumption as well as on absolute consumption.

To conclude the literature on subjective well-being, relative or reference income and absolute income are conclusive including literature such as Mcbride (2001), Ferrer-i-Carbonell (2005) and Caporale et al. (2007). Furthermore both relative and absolute income are likely to affect subjective well-being where SWB is defined as self-reported life satisfaction and happiness. How the relationship between SWB, absolute income and relative income vary among agents is examined by Caporale et al. (2007), when they examined weather the effect of relative income persisted for different age groups and for different levels of education. Despite this the literature on the latter are limited and would benefit of additional research, adding more elements to how the relationship vary among different agents. Furthermore the research on how the relationship between SWB, absolute income and relative income vary among agents on a micro level in a country would also benefit of additional research. Especially for a country such as Sweden for which no such research have been made. The closest research is made by Caporale et al. (2007) who found that the Scandinavian countries as a whole were found to be least influenced by reference income.

3. Theoretical framework

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subject, namely relative consumption and status signaling. The first of these theories would refer to standard’ envy effects implying that one are worse off when others are doing better than oneself. The second includes signal effects where information about future prospects and ambitions are considered. Assuming that the individual utility function is affected, at least in part, by relative standings of others in terms of income used for consumption of different goods. We consider the following simplified individual utility function as follows:

𝑈𝑆𝑊𝐵 = 𝐹(𝐶𝑖, 𝐶̂𝑖 ) (1) where 𝐶𝑖 is the individual’s consumption of any goods and 𝐶̂𝑖 is, typically, set as the consumption of a reference group or average. The theory behind this linked to relative standings is based on the assumption that the level of consumption of others would ultimately affect the individual’s utility, regardless of the type of goods consumed as long as the function of the good is identical. A higher consumption of any identical or higher quality good would affect the individual’s utility. Basic utility theory and the latter would imply that higher levels of consumption of others would have a negative effect for the own utility and vice versa. Deriving utility from relative consumption of any good is, typically, assumed in standard models where literature such as Duesenberry (1949), Ferrer-i-Carbonell (2005) and Caporale et al. (2007) incorporates relative standing into the utility function based on similar theories. Let us consider an example; assume that one only have two neighbors, acting as the reference group, which both consumes relatively more compared to oneself. Assume further that one neighbor have a relatively higher consumption of cars, owning two cars which have identical function and quality as the one owned by oneself, and the other neighbor consumes more of vacations enjoying two vacation weeks on a year compared to one vacation week for oneself. According to this theory the relatively higher consumption of both neighbors would have an negative effect on the individual’s utility, assuming that the different goods have an identical quality value. I.e. holding quality constant.

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Literature, imposing status signaling on the other hand, such as Martinsson et al. (2005) and Alpizar et al. (2005) would assume that relative consumption is more important for goods such as cars and houses compared to more non-positional goods such as insurance and leisure. We can think of a simplified utility function as follows:

𝑈𝑆𝑊𝐵 = 𝐹(𝛿𝑖, 𝛿̌𝑖) (2) where 𝛿𝑖 is the individual consumption of positional goods and 𝛿̌𝑖 is the relative consumption of positional goods, i.e. consumption of a reference group or average. The latter would reflect the importance of status when it comes to determining the relative position of an individual in a society. Hence, signaling a higher status would result in higher levels of reported SWB and a higher relative position in society. Implying that if one were driving around in a car associated with high status, e.g. a Rolls Royce, one would report higher levels of SWB when everyone else drove around in cars associated with lower levels of status. I.e. driving around in a Rolls Royce would signal something different about that persons social standing than a person driving an ordinary car. Although this type of setup would typically require a larger amount of information than just information about individual’s income to examine.

In order to incorporate relative standing into the utility function and linking the theory to the empirics we consider the following simplified cases. Firstly we consider previous research from Caporale at al. (2007) which assume the that utility is determined by some reference income. The authors incorporate relative standings into the utility function as follows:

𝑈𝑆𝑊𝐵 = 𝐹(𝑥𝑖, 𝑥̂𝑖 ) (3) where 𝑥𝑖 is the individual income and 𝑥̂𝑖 is the mean income of all individuals in a reference group, containing all individuals’ that live in the same region and are within 5 years younger and 5 years older as the individual in question. I.e. Caporale at al. (2007) incorporates relative standings by specifying a reference group and using the mean income of that reference group as a reference that the individual is likely to compare to. This could be considered to be a more general formulation.

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𝑈𝑆𝑊𝐵 = 𝐹(𝑥𝑖,𝑥𝑖

𝑥̂𝑖)

(4)

In this model 𝑥𝑖 is the individual income and 𝑥̂ is the average income of an reference group. 𝑖 Other literature such as Ferrer-i-Carbonell (2005), Caporale at al. (2007), Akerlof (1997), Corneo & Jeanne (1997), Knell (1999) and Ljungqvist & Uhlig (2000) have used an additive comparison utility function:

𝑈𝑆𝑊𝐵 = 𝐹(𝑥𝑖, 𝑥𝑖 − 𝑥̂𝑖) (5) Again 𝑥𝑖 is the individual income and 𝑥̂ is the average income of an reference group. Which of 𝑖 these two measurements should one than choose, additive or ratio? Well, the choice between an additive measure and a ratio measure is only a choice of the functional form of the utility function. Which one of these that are more suitable are hence most likely data specific. Discussing the theoretical differences Clark and Oswald (1998) show some theoretical differences between the additive and ratio measurement formulations, where the ratio measurement could be simpler to use with estimations if one for example would like to work with logarithmic models. Johansson-Stenman et al. (2002) makes up for one study comparing the additive comparison utility function to the ratio comparison utility function by performing some simple tests. The tests set for the functional difference concern were based on three different sets of questions with a total of 103 respondents where, in each set, the average income were elaborated with. However Johansson-Stenman et al. (2002) came to the conclusions that the ratio measurement perhaps could “performed better in terms of explaining respondent behaviour” under certain settings but that more research would be beneficial. On the other hand the additive measure would economically theoretically provide a slightly simpler model than the ratio measurement.

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Implying that a observed negative reference measure would imply that the own income would be below the reference one and that a observed positive reference measure would imply that the own income is above the reference one. The interpretation of a ratio measure would not be as simple since it would be a ratio and hence cannot take any negative values. The interpretation would rather be in terms of an ratio, for example the own income is 0,5 times the reference one or the own income is 2 times the reference one. Hence the additive measure is used for identical data specification reasons and for simplicity reasons and will be identical to equation (5). The ratio measurement could on the other hand be easier to use if estimating logarithmic models.

Furthermore this thesis is also incorporating relative standings in the more general form as the mean income of a reference group, induced by Carporale et al. (2007), similar to equation (3). The reference measure is used to strengthen the results and should be seen as a compliment to the additive measure.

4. Method

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unobserved level of utility is related to the observed personal characteristics and income.The ESS data questions for life satisfaction and happiness are, thus, both multiple choice questions where respondents arrange answers on a numbered scale from 0 to 10. 10 is set to be at the high end of the scale, making an answer of 10 imply the respondent to be fully satisfied with life.

When it comes to the framework of analyzing ordinal responses, like option responses or opinion surveys from strongly disagree to strongly agree, the ordered probit (and logit) models have come to be of widely use, see McElvey & Zavoina (1975). As discussed in Greene (2012) the logistic model could be applied just as easily since in practice the logistic and normal distributions would generally give similar results. Logistic regression is, generally, more popular in health sciences, such as epidemiology, partly because coefficients may be interpreted in terms of odds ratios. Probit models on the other hand can be generalized to account for non-constant error variances in more advanced econometric settings, such as heteroskedastic probit models. Hence probit models are more often used by economists and political scientists, see Chapel et al. (2004).

Due to the ordinal nature of the dependent variables we, firstly, exclude usage of ordinary least square, OLS, regressions. Since an OLS regression would assume that the distance between the categories are equal, not making a difference between if the dependent variable is of ordinary scale or linear scale. I.e. OLS would treat the difference between a 9 and a 10 in the same way as the difference between a 1 and a 2 and fail to capture that they are rankings. For example, if the dependent variable is happiness, an OLS will fail capturing that an increase from a 9 to a 10 would imply becoming more happy on the happy end of the scale whilst an increase from 1 to 2 would imply being more happy on the unhappy end of the scale. Secondly, because of the ordinal nature of the dependent variables I use ordered probit techniques which also are suggested by previous literature such as Oswald and Clark (1995), Macbride (2001), Ferrer-i-Carbonell (2005) and Caporale et al. (2007). Furthermore since ordered logistic techniques are assumed to give similar result I also test this by considering ordered logistic models as well.3

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Leaning on previous literature I use models similarly to Caporale et al. (2007) and Ferrer-i-Carbonell (2005) where the two dependent variables, happiness and life satisfaction, are regressed separately. Furthermore I assume, like Caporale et al (2007), that unobserved levels of individual utility are determined by observed personal characteristics and income. Greene (2012) discusses furthermore that Ordered probit models are, just as binomial probit models, built around a latent regression assuming a continuous and latent measure of the dependent variable which is given by:

yi = x i

β + ε

i (6)

where 𝑥𝑖 would be a vector of explanatory variables describing characteristics of the individual and the different income measures, absolute and relative income. The vector of parameters to be estimated is β and ε𝑖. Finally 𝑦𝑖∗ would respond to the ordinal reported scales of the dependent variable 𝑦𝑖. The equation in question does not imply a linear utility function by default, i.e. the vector of explainable variables could also contain quadratic terms.

In equation (6) 𝑦𝑖 is unobserved and what is observe is as follows:

𝑦𝑖 = 0 𝑖𝑓 𝑦𝑖∗≤ 0 (7) 𝑦𝑖 = 1 𝑖𝑓 0 < 𝑦𝑖≤ 𝜇 1 (8) 𝑦𝑖 = 2 𝑖𝑓 𝜇1 < 𝑦𝑖≤ 𝜇 2 (9) : : : 𝑦𝑖 = 𝐽 𝑖𝑓 𝜇𝐽−1 ≤ 𝑦𝑖 (10)

where the μ’s are unknown parameters to be estimated simultaneously with β. The μ-variables could be seen as a form of censoring. I.e. the μ’s represents different thresholds to be estimated simultaneously with β. The interpretation of equation 4, for example, would be as follows: the observable y takes the value 2 if the unobserved 𝑦∗ lies within the interval 𝜇

1 ≤ 𝜇2. As Greene (2012) I assume 𝜀 ~ 𝑁 (0, 1) which would give the following properties:

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Prob(𝑦𝑖 = J | x𝑖) = 1 − Φ(μ𝐽−1 − xiβ) (14)

where Φ (..) represents the cumulative distribution function. For the probabilities to be positive the following must apply:

0 < μ1 < μ2 < ··· < μ𝐽−1 (15)

The nature of the ordered probit model implies that in order to get estimations of any parameter that could be interpreted as a magnitude one must calculate marginal effects, as discussed in Greene (2012).

Marginal effects are calculated as follows: 𝜕 𝑃𝑟𝑜𝑏 (yi = 1|x𝑖) 𝜕x𝑖 = [−∅(xi ′𝛽) − ∅(𝜇 1− xi′𝛽)]𝛽𝑖 (16) 𝜕 𝑃𝑟𝑜𝑏 (y𝜕xi = 2|x𝑖) 𝑖 = [−∅(𝜇2− xi ′𝛽) − ∅(𝜇 1− xi′𝛽)]𝛽𝑖 (17) : : 𝜕 𝑃𝑟𝑜𝑏(yi = 𝐽|x𝑖) 𝜕x𝑖 = 1 − ∅(𝜇𝐽− xi ′𝛽)𝛽 𝑖 (18)

The general output from the ordered probit regression model does not include the common F-test or R2 value, typically found in an OLS regression.4 Hence, a different method of determining whether the included interaction variables has any explanatory power in explaining the model must be considered. Specifically a Wald test of composite linear hypotheses about the parameters of the two regression models is considered. The Wald test tests whether the interaction variables, taken as a whole, are significant by testing weather the interaction

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coefficients are simultaneously zero. The Wald test statistic is stated as follows (Judge et al. 1985):

𝑊 = (𝑅𝑏 − 𝑟)′(𝑅𝑉𝑅′)−1 (𝑅𝑏 − 𝑟) (19) The estimated coefficient vector is denoted b and the estimated variance –covariance matrix is denoted V. Rb = r denote the set of q linear hypotheses to be tested jointly. Moreover a chi-squared distribution with q degrees of freedom is used for computation of the significance level of the hypothesis test as follows:

W ∼ 𝑋𝑞2 (20)

Thus, the null hypothesis of that all estimated coefficients of interaction are jointly equal to zero is tested against the alternative hypothesis that all estimated coefficients of interaction are jointly equal to zero ( H0: jointly = 0 against HA: jointly ≠ 0).

5. Data

For the purpose of this thesis data from The European Social Survey (ESS) is used. The European Social Survey is a cross national survey across more than thirty countries in Europe which is conducted every two year starting in 2001. The ESS is an academically driven survey which is financed by the European Commission’s framework Programs, the European Science Foundation (EFS) and by the founding national councils in the participating countries. This is due to the ESS legal status of European Research Infrastructure Consortium which was announces in 2013. The survey consists of face-to-face interviews which measure beliefs, attitudes and behavior patterns. One of the main goals set by the ESS is to improve a higher standard of cross national research in Europe. The European Social Survey database is a database that is free of charge and non-commercial which can easily be accessed and downloaded from the web. To be specific the ESS data consists of 34 countries in total that have participated in the ESS-survey’s.5 This thesis uses data from Sweden and from the survey rounds of 2012 and 2014.

From the ESS-data I obtain the two dependent variables ‘life satisfaction’ and ‘happiness’ as discussed before. Moreover, respondent’s income is obtained as the household’s net total income, all sources, on a monthly basis. The specific question asked is: “Using this card, please

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state which category describes your household's total income. If you don't know the exact figure, please give an estimate.” The respondent’s income is, moreover, obtained after tax and other compulsory deductions. The corresponding answering card used for this question is showed in table 1 below, where income is measured in SEK. Hence, the individual’s total net household income is measured in deciles. Hence, we can see that income is recorded as intervals rather than exact income which to an extent is a measurement error. In order to obtain a more convenient income measure which could be more easily interpreted a new income variable is created. Making the individual’s total net household income, all sources, to be equal to be the middle income of the corresponding income group, see Caporale et al. (2007) and Macbride (2001). This process is shown by table 1. However the midpoint of the interval stating an income above 49 000 SEK cannot be directly observed since no upper level is defined. The midpoint is instead estimated by using statistics from Statistics Sweden.6

Table 1. Income Deciles

Let us consider an example to illustrate this procedure of created midpoints. Cconsider a total net household income of 23 000 SEK for individual i which falls into income group F (22 000– 24 999), then according to the definition of the new variable individual i’s income will be recorded as the middle income of the corresponding income group, namely 23 500. Moreover

6 Statistics Sweden is an administrative Swedish agency set to supply statistics for decision making, debate and research. According to Statistics Sweden the median net income of households’ with an income of 49 500 SEK and more is 57 506 SEK for 2012 and 57 468 for 2014, which is the top highest income decile stated by Statistics Sweden. Rounding of these two numbers into the nearest hundredth gives an estimated midpoint of 57 500 SEK.

Income Deciles Created ‘Midpoints’

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this thesis uses data from the survey rounds 2012 and 2014 because using this specific rounds would make the number of observations as large as possible without adding additional measurement errors. In general all participating countries have different income intervals measuring a household’s total net income and more relevantly this is also the case for the different survey rounds within a country.

It is helpful to consider a simple example to illustrate the possible merging problematic if having different income intervals for different years. Consider two years, A and B, which use different income intervals, and there are two income intervals for each year, namely high and low income. The income intervals for year A would be defined as follows: ‘Low income’ including incomes up to 24 999 (currency) and ‘High income’ including incomes from 25 000 (currency) and more. The income intervals for year B are: ‘Low income’ including incomes up to incomes up to 22 999 (currency) and ‘High income’ include incomes from 23 000 (currency). Now one can see the nature of the problem since individuals having an income of 24 000 (currency) in year A would fall into a lower income category whilst similar individuals in year B would fall into the higher. Choosing survey data with perfectly identical income intervals would not encounter this problem.

Concerning Sweden, I find that the survey rounds for 2012 and 2014 actually use the exact identical income intervals. Thus, this can be used to make the number of observations as large as possible without adding additional errors of measurement which would happen if two survey rounds with different income intervals are chosen. I.e. the reason to why the survey rounds of 2012 and 2014 are specifically included is, hence, outlined by the discussion considered above. Moreover since two different survey rounds from two different years are used I consider a price index. The prices of 2012 are calculated into the prices of 2014 by using the ‘inflation’ deflator (nominal GDP/real GDP) for each year. In additional to this I also control for any differences by running the regressions separately for each year and compare the results.7

The nature of income comparisons and the effect on subjective well-being depends in some way on the actual comparison segment. If we tend to compare income with each other than who compares to whom? Clark & Senik (2010) made this to be their topic for their paper which is based on the third wave of the European Social Survey (ESS) covering 18 European countries,

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including Sweden. The authors starts out by examining some key income-comparison questions which could be found for these specific ESS survey rounds. Especially two questions asked for these ESS survey rounds are very useful when it comes to determining income comparisons. The first question states the following “How important is it for you to compare your income with other people’s incomes?’ Individuals are asked to answer by using a show card reaching from 0 to 5, where 0 is not at all important and 6 is very important. The answers found that 25% of the respondents did not think comparing were important at all (answering 0 on the scale) and 28% though comparing are very important (with answers of 4 to 6 on the scale). The second question states: “Whose income would you be most likely to compare your own with? Please choose one of the groups on this card: Work colleagues/ Family members/ Friends/ Others/ Don’t compare/ Not applicable/ Don’t know”. The results revealed that a majority (36,3 %) compare themselves to their work colleagues and that more than a third (35,9 %) of the respondents do not compare. More specifically 5,8 % compare to family members, 14,9 % to friends and 7,1 % to others. The authors also found that those who have a relatively lower income tend to compare their incomes more whilst those who are self-employed tend to compare their incomes significantly less compared to those who are employees. Unfortunately these questions are not available for the two latest waves of the European Social Survey (ESS) which are used by this thesis.

While it is useful to know something about the general intensity of income comparison, as described above, Clark & Senik (2010) further investigatesto whom people actually compare.

According to Clark & Senik (2010) the reference group would be endogenous, at least to an extent, which appears reasonable. A reference group to whom one compares are hence likely to

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majority of empirical papers such as Clark and Oswald (1996), MacBride (2001), Ferrer-i-Carbonell (2005) Luttmer (2005) and Carporale et al. (2007) have simply imposed a certain reference group which is made relevant for income comparison purposes.8

The induction of a certain reference group, made relevant for income comparison purposes, is quite useful. The reference group for this thesis is hence specified to mainly follow Carporale et al. (2007) which base their paper on similar data as this thesis and because the specification of the reference group is is made relevant for income comparison purposes similar to this thesis. Carporale et al. (2007) in their turn follows firstly McBride (2001) defining the reference group to include all individuals who are in the age range of 5 years younger and 5 years older than the individual concerned and, secondly, Ferrer-i-Carbonnell (2005) defining the reference group to also include those living in the same region.

5.1 Variables

This thesis is incorporating relative standings in two ways, as an additive measure and as the mean income of a reference group. Leaning on Ferrer-i-Carbonell (2005) we consider the following additive comparison utility function:

𝑈𝑆𝑊𝐵 = 𝐹(𝑥𝑖, 𝑥𝑖 − 𝑥̂𝑖) (21) where 𝑥𝑖 is the individual income and 𝑥̂ is the average income of an reference group defined 𝑖 as all individuals that live in the same region and are within 5 years younger and 5 years older as the individual in question. Moreover this thesis is additionally incorporating relative standings using a reference measure as well to strengthen the results. Leaning on Carporale et al. (2007) relative standings are incorporated into the utility function as follows:

𝑈𝑆𝑊𝐵 = 𝐹(𝑥𝑖, 𝑥̂𝑖 ) (22) where 𝑥𝑖 is the individual income and 𝑥̂𝑖 is the average income of all individuals in a reference group, containing all individuals that live in the same region and are within 5 years younger and 5 years older as the individual in question. Furthermore reference income is expected to exert a negative effect on the two dependent variables, ‘individual happiness’ and ‘life satisfaction’, whilst absolute income is expected to exert a positive effect, as suggested by Carporale et al. (2007). On the other hand the sign of the additive measure is expected to take

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opposite sign. Implying that the additive measure is expected to exert a positive effect on the two dependent variables, ‘individual happiness’ and ‘life satisfaction’.

One way to examine how the relationship between absolute income, relative income and SWB varies among agents is by introducing ‘interaction variables’. Adding interaction terms to a regression model can expand understanding of the relationships among the variables in the

model allowing more hypotheses to be tested.

An interaction variable is basically a variable, of

interest, interacted with a another variable which can be constructed in a number of ways. A rather simple way to construct an interaction variable is to simply multiply the variable of interest with a preferred background variable. Another way is to let some software, such as STATA, interact the variable of interest with the background variable using a specific command. Let us consider an example, assume that we want to examine how an increase in absolute income affect SWB when living with a partner. Here we can construct a variable defined as the variable partner times absolute income or interacting the variable partner with absolute income using the software. Both would suggest how SWB is effected if one lives with a partner and absolute income is increased.

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As discussed by Greeta et al (2005) relative income would, at least in part, affect subjective well-being differently depending on the distance of comparative others. In order to examine if there are any differences depending on population size the dummy variable region is created. The variable states in which region, in Sweden, the respondent lives in where an exact summery of the population for each region can be found under the appendix section. Moreover there are two regions with a relatively higher population density, Stockhoms Län and Skånes Län. More specifically Stockhoms Län recorded a population density of 336,9 inhabitants per square kilometer (2014) and Skånes Län 117,5 recorded inhabitants per square kilometer (2014). The dummy variable created for the different regions take the value 1 if the respondent live in a region with a relatively higher population density, namely in either Stockhoms Län or Skånes Län, and the value 0 if not.9

Leaning on Caporale et al. (2007) where individuals with higher levels of education were split into one group and those with low levels of education into another group, a dummy variable for different levels of education is created. The specific question asked about education is stated as follows: “About how many years of education have you completed, whether full-time or part-time? Please report these in full-time equivalents and include compulsory years of schooling”. The variable is hence numerical and the idea is to capture different stages of the Swedish education system by introducing a dummy variable. The dummy variable, labeled ‘education’, take the value 1 if the respondent have completed more than 12 years of education, post ‘gymnasial level’. The dummy variable take the value 0 if the respondent have completed education up to 12 years which would refer to ‘gymnasier level’ in Sweden.

Caporale et al. (2007) defines additional age groups for individuals under 40 years of age and for those above which were run as two separate regression. The equivalent variable defined for this thesis is based on the already existing variable Age which is a numerical variable stating the age of the respondent, from which three dummy variable is created. In addition to Caporale et al. three different age groups are defined where the first age group represents people as ‘young’ and include respondents under 30 years of age. The second age group is set to represents people in ‘midlife’, including respondents between 30 to 65 years of age. The third age group represents ‘old’ people, including respondents over 65 years and older. Thus, three

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different age groups are identified. 10 The first dummy variable, labeled ‘young’ takes the value 1 if respondents fall into the first age group and 0 if not. The second dummy variable, labeled ‘old’, takes the value 1 if respondents fall into the third age group and 0 if not. Respondents between 30 and 60 years of age is used as a reference.

Economic worries appear to be especially important among lower income persons, Easterlin (1974) . In order to examine the effects exerted by the different income measure due to different levels of income a dummy variable is created. The dummy variable is based on the re-coded income variable where the midpoint of each income decile is used to create a continuous variable. The fifth and middle decile, corresponding to a midpoint income of 23 500 SEK, is used as a threshold. Thus, creating two income groups, ‘low’ and ‘high’, were the dummy variable take the value 1 if the respondent record an income above the threshold and 0 if not.

Leaning on Duesenberry (1949), Easterlin (1973), Mcbride (2001) the following variables are identified. The variable unemployment takes the value 1 if the respondents answer to the following question is true: “Have you ever been unemployed and seeking work for a period of more than three month?” and take the value 0 if not. The variable for gender take the value 0 if male and 1 if female. The variable partner take the value 1 if the respondent is currently living with a husband/wife/partner and the value 0 if not. Furthermore based on the idea of shifting preferences of individual’s social, family and economic circumstances, discussed in literature such as Alesina et al. (2004) and Caporale et al. (2007), I want to add an additional variable that concerns country of birth. I.e. I want to examine if shifting preferences could be recognized by examining how the different income measures affect SWB for people born in Sweden respectively to people that are born elsewhere. In order to examine effects relating to birth country, i.e. born in another country than Sweden, the variable country of birth is created. The variable take the value 0 if respondent is born in Sweden and 1 if not.

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5.2 Descriptive statistics and Empirical model

Table 3: Descriptive Statistics

Variable Obs Mean Std. Dev. Min Max

Happiness 2724 7,846 1,523 0 10 Life Satisfaction 2725 7,869 1,688 0 10 Absolute Income 2487 32186 14815 5500 57500 Reference Income 2487 32088 6763 5500 57500 Relative Income 2481 21,386 14733 -39437,51 48972,47 Gender 2730 0,498 0,500 0 1 Age 2727 48,456 19,468 15 97 Region 2730 0,520 0,500 0 1 Education 2730 13,11 3.501 0 31 Partner 2726 0,623 0,485 0 1 Unemployment 2716 0,255 0,436 0 1 Country of birth 2730 0,866 0,340 0 1

As observed from table 3 the individuals in the sample, on average, have a happiness level of 7,846 out of 10. Given that 5 is defined as neither unhappy or happy the individuals in the sample appear to be happy. Moreover a similar number is observed for life satisfaction, more specifically 7,869 implying that the individuals in the sample are a slightly more satisfied with their lives, at the moment, than they are happy. The average estimated total net household income for the sample is 32186 SEK and the estimated average income of the reference group is 32 088 SEK. Furthermore relative income is observed to have a maximum value of 48972,47 and a minimum value of -39437,51. The mean value of relative income imply that the average difference, measured in SEK, between individual i:s income and the average income of all individuals within individual i:s reference group is 21,386 SEK.

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To get a broader view of the model and the variables included the following could be visualized, where the dependent variable represent ‘life satisfaction’ and ‘happiness’ respectively: 𝐷𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 = (23) 𝛽0+ 𝛽1× [𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐼𝑛𝑐𝑜𝑚𝑒] + 𝛽2× [𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐼𝑛𝑐𝑜𝑚𝑒] + 𝛽3× 𝑃𝑎𝑟𝑡𝑛𝑒𝑟 + 𝛽4× 𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝐵𝑜𝑟𝑛 + 𝛽5× 𝐺𝑒𝑛𝑑𝑒𝑟 + 𝛽6× 𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 + 𝛽7× 𝑅𝑒𝑔𝑖𝑜𝑛 + 𝛽8× 𝐸𝑑𝑢𝑐𝑎𝑡𝑖𝑜𝑛 + 𝛽9× 𝐴𝑔𝑒 + 𝛽10× 𝐴𝑔𝑒2 + 𝛽11× [𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝑃𝑎𝑟𝑡𝑛𝑒𝑟 + 𝛽12× [𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝐵𝑜𝑟𝑛 + 𝛽13× [𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝐺𝑒𝑛𝑑𝑒𝑟 + 𝛽14× [𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 + 𝛽15× [𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝑅𝑒𝑔𝑖𝑜𝑛 + 𝛽16× [𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝐸𝑑𝑢𝑐𝑎𝑡𝑖𝑜𝑛 + 𝛽17× [𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝐴𝑔𝑒𝑔𝑟𝑜𝑢𝑝 + 𝛽18× [𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝐼𝑛𝑐𝑜𝑚𝑒𝑔𝑟𝑜𝑢𝑝 + 𝛽19× [𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝑃𝑎𝑟𝑡𝑛𝑒𝑟 + 𝛽20× [𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝐵𝑜𝑟𝑛 + 𝛽21× [𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝐺𝑒𝑛𝑑𝑒𝑟 + 𝛽22× [𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝑈𝑛𝑒𝑚𝑝𝑙𝑜𝑦𝑚𝑒𝑛𝑡 + 𝛽23× [𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝑅𝑒𝑔𝑖𝑜𝑛 + 𝛽24× [𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝐸𝑑𝑢𝑐𝑎𝑡𝑖𝑜𝑛 + 𝛽25× [𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝐴𝑔𝑒𝑔𝑟𝑜𝑢𝑝 + 𝛽26× [𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐼𝑛𝑐𝑜𝑚𝑒]#𝐼𝑛𝑐𝑜𝑚𝑒𝑔𝑟𝑜𝑢𝑝 + Ɛ𝑖

6. Result

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Note: *** , ** & * denote statistically significant at 1%, 5% and 10%, respectively.

Table 4 shows the marginal effects of the separate regressions, where the marginal effects are presented as the average of J from 1 to 10 over individuals and the interaction variables are excluded11. Looking at the first part of table 4 and the separate effects on both ‘happiness’ and ‘life satisfaction’, one can observe significant estimated marginal effects for the variables

absolute income, relative income, partner and unemployment. The estimated marginal effect

for absolute income suggest that increased absolute income would on average have a positive effect on self-reported individual happiness and life satisfaction, known as SWB. This is also true for the estimated marginal effect of relative income, defined as an additive measure, which suggest that increased relative income would have an positive effect on SWB. Furthermore the estimated marginal effect for unemployment is observed to be negative. Hence unemployment,

11Since it otherwise would be 10 marginal effects for each variable and individual to be presented as seen from equations 16 to 18 which

would be rather messy and uninformative to present.

Table 4 – Marginal effects; ordered probit. Interactions excluded.

(Additive Measure)

[’Happiness’]

[’Life

Satisfaction’]

Variables Coefficient |z| Coefficient |z|

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unemployed and seeking work for more than three months, would on average affect SWB negatively. The estimated marginal effects for country of birth and education are only observed to be significant when happiness is used as the dependent variable. The estimated marginal effect for age, on the other hand, is observed significant only for when life satisfaction is used as the dependent variable. By considering the magnitude of these marginal effect one can observe that relative income and absolute income would have the largest effect on SWB and

unemployment would have the smallest, although in the opposite direction.

The second part of the results presented in table 4 concerns the reference measure as a complement to strengthen the results. One can observe similar estimated average marginal effects both in terms of the number of significant estimated marginal effects and in terms of similar magnitudes of these effects. Hence the results observed for the reference measure are similar to the results of the additive measure, with the distinction that the reference measure take opposite signs as predicted. These separate effects, from table 4, does not surprise since previous literature such as Mcbride (2001), Greeta et al (2005) and Caporale et al. (2007) exhibit similar results. Although Caporale et al. (2007) found unemployment to have a positive effect on life satisfaction which appeared stronger for the Scandinavian countries.

Table 5 – Ordered probit regressions. Relative Income and Reference Income, interactions included.

Relative Measure

[’Happiness’] [’Life Satisfaction’]

Variables Coefficient |z| Coefficient |z|

Absolute Income 0,00021** 2,74 0,000158*** 3,41 Relative Income 0,000011 0,31 0,000021 0,77 Partner 0,00078*** 5,10 0,00037*** 4,84 Country of birth 0,00029** 1,97 0,00097** 2,22 Gender 0,00035 0,21 0,000959 0,76 Unemployment -0,00186 -0,88 -0,00058** -2,18 Region 0,00074* 1,68 -0,000587 -0,79 Education 0,00011 0,36 -0,000004 -0,20 Age 0,000401* 1,35 0,000721** 2,68 Age2 0,000059 0,08 0,000087 0,17

Absolute Income Interaction

Partner 0,0001213* 1,61 0,0001403* 1,71

Single 0,0005251* 1,87 0,0015112*** 3,05

Born in Sweden 0,0002225** 2,77 0,0006686* 1,76

Born elsewere 0,0006934* 1,61 0,0019044* 2,01

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Male 0,0002303* 1,72 0,0007623*** 3,01

Unemployment 0,0005394* 1,70 0,0005263* 1,75

Employed 0,0001854** 2,11 0,0002229* 1,88

High density region 0,0003154* 1,76 0,0011651* 1,59

Low density region 0,0001251* 1,74 0,0006273* 1,95

High education 0,0002456** 2,52 0,0008385** 2,44

Low education 0,0003435* 1,84 0,0009145** 2,86

Income group (high) -0,0000835 -0,78 0,0000175 0,07

Income group (low) -0,0000108 -0,55 -0,0000942 -0,77

Young 0,0002788** 2,19 0,0008479*** 3,29

Middleaged 0,0004751** 2,88 0,0013579*** 3,96

Old 0,0001899** 2,38 0,0005969* 1,59

Relative Income Interaction

Partner 0,00000944** 2,06 0,00000279** 1,83 Single 0,00000938** 2,84 0,00000276* 1,70 Born in Sweden 0,00000440** 2,38 0,00000405** 2,33 Born elsewere 0,00000147* 1,62 0,00000131** 1,42 Female 0,00000646* 1,79 0,00000162* 1,94 Male 0,00000435* 1,72 0,00000148* 1,88 Unemployed 0,00000104* 1,92 0,000000298** 2,64 Employed 0,00000372* 1,74 0,000000307** 2,83

High density region 0,00000660* 1,79 0,000000125 0,25 Low density region 0,00000486* 1,69 0,000000233* 1,66

High education 0,00000517*** 2,91 0,0000164** 2,13

Low education 0,00000660** 2,12 0,0000174** 1,95

Income group (high) 0,000000143 1,04 0,00000165 0,45

Income group (low) 0,000000120 0,58 -0,00000184 -0,48

Young 0,00000584* 1,76 0,00000173** 1,78 Middleaged 0,00000985** 1,98 0,00000266** 2,66 Old 0,00000359* 0,50 0,00000140** 2,37

Reference Measure

Absolute Income 0,00018** 2,89 0,00026*** 3,11 Reference Income -0,00010 -1,11 -0,00024* -1,89 Partner 0,00068*** 5,78 0,00037*** 3,99 Country of birth 0,00031** 2,33 0,00036** 2,59 Gender 0,00089 0,09 0,00102 0,78 Unemployment -0,00021 -0,99 -0,00073** -1,88 Region 0,00048* 1,91 -0,00088 -0,81 Education 0,00051 0,39 0,00044 0,25 Age 0,00042* -0,17 0,00078** -1,87 Age2 0,000041 0,24 0,000109 0,33

Absolute Income Interaction

Partner 0,0000458* 1,67 0,0000584* 1,62

Single 0,0000988* 1,84 0,0002081** 2,02

Born in Sweden 0,0000474** 2,18 0,0000955** 2,22

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Note: *** , ** & * denote statistically significant at 1%, 5% and 10%, respectively.

Table 5 includes the results for the ordered probit regressions when interaction variables are included. The marginal effects are presented as the average of J from 1 to 10 over individuals. Moreover in this model where interactions are included marginal effects of the different income measures are presented separately for all interactions. So that, for example, the marginal effects for absolute income are presented separately for those with and without partners, for men and women and so forth12. Regarding the interaction effects on ‘happiness’ and ‘life satisfaction’

12 This is because interaction terms cannot vary independently depending on the variables they consist of, and

therefore do not have their own marginal effects, Chunrong & Norton (2003). It is the difference between marginal

effects between different groups that should be interpret rather than the interaction coefficients.

Female 0,0000128* 1,59 0,0000359* 1,64

Male 0,0000058* 1,47 0,0000298* 1,81

Unemployment 0,0000098* 1,57 0,0000127* 1,63

Employed 0,0000140* 1,87 0,0000244* 1,72

High density region 0,0001458* 1,84 0,0002540* 1,77

Low density region 0,0000389* 1,69 0,0001511* 1,73

High education 0,0001199** 2,06 0,0002638** 2,89

Low education 0,0002225* 1,87 0,0003289** 2,86

Income group (high) -0,0000258 -0,78 0,0000578 0,78

Income group (low) 0,0000805 0,47 0,0000657 0,69

Young 0,0001287** 1,99 0,0001358** 2,08

Middleaged 0,0005898* 1,87 0,0006221* 1,68

Old 0,0002874** 2,88 0,0002599*** 3,96

Reference Income Interaction

Partner/ -0,0000208** -2,19 -0,0000255* -1,79 Single/ -0,0000125* -1,59 -0,0000148* -1,69 Born in Sweden/ -0,00000127** -2,99 -0,00000254* -1,87 Born elswere/ -0,00000124** -2,89 -0,00000129* -1,74 Female/ -0,00000590* -1,88 -0,00000741* -1,82 Male/ -0,00000178* -1,66 -0,00000320* -1,71 Unemployment/ -0,00000150* -1,89 -0,00000186* -1,88 Employed / -0,00000946* -1,81 -0,00000203* -1,76

High density region/ -0,000000124 -0,35 -0,00000254* -1,68 Low density region/ -0,000000132* -1,46 -0,00000149* -1,49

High education/ -0,0000178* -1,99 -0,00000320** -2,78

Low education/ -0,0000211* -1,95 -0,00000753** -2,22

Income group (high)/ 0,00000166 0,74 0,00000210 1,11 Income group (low)/ -0,00000830 -0,19 -0,00000158 -0,47

Young -0,00000188** -1,77 -0,00000478* -1,66

Middleage -0,00000247** -2,10 -0,00000854* -1,69

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when absolute income is interacted with other variables, one can observe significant estimated marginal effects for all interactions except for income group (high) and income group (low), which are observed non-significant. Moreover the significant estimated marginal effects are all observed to be positive, implying that an increase in absolute income would have a positive effect on SWB. By observing the magnitude of the estimated marginal effects one can observe that for example an increase in absolute income would on average lead to a small increase in happiness if the respondent lives with a partner or wife/husband, cetris paribus. This suggest that absolute income is, on average, more important for SWB if one is single. The estimated marginal effects for country of birth suggest that an increase in absolute income lead to a smaller increase in SWB if the respondent is born in Sweden, cetris paribus. Hence, absolute income is on average more important for SWB if one is not born in Sweden.

Furthermore the results suggest that an increase in absolute income is on average less important for SWB if one is younger than 30 years of age or over 65 years of age, compared to an age between 30 and 65. This suggest that absolute income is on average more important to SWB if one is ‘middle-aged’, i.e. between 30 and 65 years of age. The estimated marginal effects for

high density region and low density region are observed to be significant for when both

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The interaction effects on ‘happiness’ and ‘life satisfaction’ when relative income is interacted with other variables are observed to have significant estimated marginal effects for all interactions except for income group (high) and income group (low) which are observed non-significant. The only other estimated marginal effect that is observed non-significant when ‘life satisfaction’ is used as the dependent variable is high density region. All significant estimated marginal effects are observed to be positive implying that an increase in relative income would have a positive effect on SWB. Looking at the magnitudes of the estimated marginal effects for

partner and single one can observe a slightly higher marginal effect for partner. Suggesting

that an increase in relative income lead to a higher increase in SWB if the respondent lives with a partner or wife/husband compared to if not living with a partner. This suggest that relative income is, on average, more important for SWB for those living with a partner, cetris paribus. The results for female and male suggest that relative income is more important for females. I.e. an increase in relative income would have a larger marginal effect on SWB if female compared to if being male. The estimated marginal effects for high density region and low density region are both observed to be significant when happiness is used as the dependent variable, but not for life satisfaction. The estimated marginal effect for high density region are observed non-significant when life satisfaction is used as the dependent variable and a result could not be established. The results suggest that an increase in relative income lead to a larger increase in happiness if the respondent lives in a region with high population density compared to living in a region with lower population density, cetris paribus. Hence suggesting that relative income is on average more important for happiness if one live in a region with high population density. The results regarding employed and unemployed suggests that an increase in relative income lead to a larger increase in SWB if one are employed. Hence relative income is on average more important if employed, cetris paribus.

Moreover the estimated marginal effects for education suggest that an increase in relative income lead to a larger increase in SWB if the respondent have completed up to 12 years of full time studies compared to if not, cetris paribus. Hence relative income is on average a larger effect on SWB when having a lower level of education, cetris paribus. The result regarding

country of birth suggest that an increase in relative income lead to a higher increase in SWB if

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age, compared to being younger than 30 or over 65 years of age. This suggests that relative income is, on average, more important if one is ‘middle-aged’, cetris paribus. Furthermore an increase in relative income would have the second largest impact on SWB if being ‘young’, under 30 years of age. Leaving an increase in relative income to have the smallest impact on SWB if being ‘old’, over 65 years of age. Moreover the result suggests that relative income is, on average, less important for SWB if being unemployed and seeking work for more than three months. Implying that an increase in relative income on average is more important for SWB if being employed, cetris paribus. Finally the estimated marginal effects for the interactions

Income group (high) and income group (low) are observed to be strongly non-significant and a

result could not be established.

In order to validate and strengthen the results of the additive measure case we consider the bottom part of table 5 were the results for the reference measure are observed. The results observed for the reference measure are identical to the results of the additive measure, as seen from table 5. The results for the additive measure are hence backed up by the results presented in the lower section of table 5 concerning the reference measure which strengthens the overall results. Finally the test statistic for the Wald test was found to be significant on a 5 % significant level for when ‘happiness’ was used as the dependent variable and significant on a 1 % significant level when ‘life satisfaction’ was used as the dependent variable. Thus, we can reject the null hypothesis of that all estimated parameters for the interaction variables is equal to zero. Implying that the included interaction variables have explanatory power in explaining the model and that it could be motivated to include the interaction variables in the models.

7. Discussion

References

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